Linear discriminant
analysis
Linear discriminant analysis is closely
related to ANOVA (analysis of variance) and regression analysis, which
also attempt to express one dependent variable as a linear combination
of other features or measurements. In the other two methods however,
the dependent variable is a numerical quantity, while for Linear discriminant
analysis it is a categorical variable.
Linear discriminant analysis and the related
Fisher's linear discriminant are methods used in statistics and machine
learning to find the linear combination of features which best separate
two or more classes of objects or events. The resulting combination
may be used as a linear classifier, or, more commonly, for dimensionality
reduction before later classification.
Linear discriminant analysis is also closely related to principal component
analysis (PCA) and factor analysis in that both look for linear combinations
of variables which best explain the data. Linear discriminant analysis
explicitly attempts to model the difference between the classes of data.
PCA on the other hand does not take into account any difference in class,
and factor analysis builds the feature combinations based on differences
rather than similarities. Discriminant analysis is also different from
factor analysis in that it is not an interdependence technique : a distinction
between independent variables and dependent variables (also called criterion
variables) must be made.
Linear discriminant analysis
works when the measurements made on each observation are continuous
quantities. When dealing with categorical variables, the equivalent
technique is Discriminant Correspondence Analysis.
In marketing, discriminant
analysis is often used to determine the factors which distinguish different
types of customers and/or products on the basis of surveys or other
forms of collected data.
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